The pair of points (g, -1) and (2, 5) lie on a line with a slope of 3/2
. What is the value of g?
To find the value of g, we need to use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
We are given that the slope of the line is 3/2.
Now we can use the point-slope formula to find the equation of the line. Given two points (x₁, y₁) and (x₂, y₂) on a line, the slope is given by m = (y₂ - y₁) / (x₂ - x₁).
Let's use the points (g, -1) and (2, 5) to find the slope:
m = (5 - (-1)) / (2 - g)
m = (5 + 1) / (2 - g) = 6 / (2 - g) = 3/2
Now we can solve for g:
6 / (2 - g) = 3/2
Cross multiplying, we get:
6 * 2 = 3 * (2 - g)
12 = 6 - 3g
3g = 6 - 12
3g = -6
g = -6 / 3
g = -2
Therefore, the value of g is -2.